Remark 3.4 
The inner balayage \(\mu ^A\)  is in general not concentrated on the set \(A\)  itself, but on its closure \(\overline{A}\) , and this occurs even for the Newtonian kernel on \(\mathbb {R}^n\) , \(n\geqslant 3\) , and \(A:=B_r:=\lbrace |x|<r\rbrace \) , \(r\in (0,\infty )\) . Indeed, for any \(\mu \in \mathfrak {M}^+_{B_r^c}\) , we have \(S(\mu ^{B_r})=\lbrace |x|=r\rbrace \)  (see [1]}), and hence actually
\(S(\mu ^{B_r})\cap B_r=\varnothing \) .

